The three episodes that covered basic particle physics were first released in September 2018 and can be downloaded here:
Up and Atom: Dank Memes and Atomic Physics
Can you tell your quarks from your elbow? If not, never fear, because these episodes will be your guide to particle physics, and, specifically, what’s called the Standard Model. Has absolutely nothing to do with the catwalk. Soon, we’ll get into particle physics beyond the standard model. There’s a good chat-up line for that…
In 1936, particle physicists felt pretty pleased with themselves. They’d discovered the three major component particles that made up the atom — the neutrons and protons in the nucleus, and the electrons that orbited around the nucleus — and they were in the process of measuring the properties of these particles. Who knows what kind of technological applications and scientific understanding could be gained — now that the fundamental building blocks of matter were observed and catalogued, we would surely get an understanding of, well, more or less everything that could be understood.
Then, some physicists — Carl Anderson and Seth Neddermeyer — noticed that there was a particle in cosmic radiation that they couldn’t explain. It curved in a magnetic field, so it was a charged particle — it felt electromagnetic forces, so it must have an electrical charge. What is charge? You can get hung up on the definition: I think it’s helpful to think of it like an electrical mass. The mass of an object tells you how much gravity pulls on it. The charge of an object tells you how much the electromagnetic force pulls on it. So the new cosmic ray particle was charged. But it didn’t curve like an electron, and it didn’t curve like a proton. They’d discovered something new — and, before too long, the young physicists involved had won a Nobel prize, and the particle they’d found — the Muon — was being studied as a whole new field in itself. But it completely upended the model — the theory — that particle physicists had about what existed in the Universe. So much so, that when the physicist I I Yabi — who would later have a Nobel Prize of his own — heard that the muon had been discovered, he quipped “Who ordered that?” Later, physicist Willis Lamb in 1955 joked that — back in the day, discovering a new particle was rewarded with a Nobel Prize. Now it should be punished by a $10,000 fine.
Particle physics is a strange field for people who want the world to be neat and orderly. There are dozens of different fundamental particles — so much so that they’re often referred to as a particle zoo. Physicists, in fits of creative ecstasy, have given them exotic and amusing names — the strange quark, the electron neutrino, the tau particle… Many of these particles don’t last for very long. The muon, which exists for 2.2 millionths of a second, is considered pretty stable compared to some of its fellow subatomic particles. (Incidentally, 2.2 millionths of a second is also the exact length of my good mood when I wake up on a Monday morning, before the grim horror dawns once again.)
And particle physicists are also very strange creatures. They love things to be neat and tidy, and organizing their zoo into little families and groups in a way they can understand. They want a Standard Model that will explain all of the different properties of these particles. But they also love nothing more than to spend billions of dollars smashing particles together at ridiculously high energies, creating massive cascades of subatomic particles as debris from the collision, in the hope of making new things to scratch their heads over. Things that don’t fit into any family or categorization. Things where we can legitimately question… who ordered that?
First, I’m going to try to explain the Standard Model of particle physics. In the next episode, we’re going to talk about possible developments “Beyond the Standard Model” — a field of study which is literally abbreviated as BDSM. But, of course, before you get into BDSM, you need to understand vanilla particle physics. And for that, we really need a history of atomic physics. So let’s make sure that we’re all on the same page.
Everything in the world around us is made up of molecules. For example, water is a molecule. Molecules themselves turn out to be multiple atoms bound up together.
Atom theory has a long history, stretching all the way back to the Greek philosopher Democritus. He is usually credited as being the first one to propose that everything was made up of tiny, indivisible parts — and to relate the properties of the whole to the properties of the atoms. Democritus was known as the “laughing philosopher” because, apparently, he was constantly mocking others and laughing at human folly. So I feel like we’re well within our rights to laugh at him, because his theory was far from correct: he thought that water atoms were very slippery, while iron atoms were very hard, and of course we know that this isn’t the case at all. But Democritus gets some credit for suggesting that things aren’t an elemental continuum.
Because, although it’s tempting to laugh at this man who was called “The Mocker” by his fellow citizens — let’s face it, his real nickname is probably much worse — he did realize something that’s incredibly counter-intuitive. Even today, you can see people on some of the darker fringes of the internet saying that “there’s no such thing as an atom, no one has ever seen one”; and while that’s patently false, it’s true if you’re talking about naked-eye vision. The world around us appears to be made up of elements; such that if you were going around, you’d pick up on it, right? This is air-stuff, this is water-stuff, this is plant-stuff, this is rock-stuff. If you characterise objects by their macrophysical properties — the properties on the scale of things we can see — then it doesn’t make sense to lump together some of the things we have to. If you take mostly carbon, hydrogen, oxygen and some traces — you can get wood, or you can get people. Just carbon alone can give you either graphite: a soft, electricity-conducting, opaque rock — or diamonds, a hard, shiny, transparent, electrically resistive substance. Yet both of these substances are made of more or less precisely the same thing.
So Democritus was right to point to atoms, but wrong in deciding that the properties of a substance depend on the atom itself. After all, we know that a hydrogen atom is equally happy to be a part of water H2O, or making up oil in hydrocarbons. It’s all about the chemical bonds between atoms. There are different kinds of atoms — and scientists in the 18th and 19th century were beginning to realize that there were some substances that were, in a sense, fundamental — they could react with each other, and things could be broken down into these ‘elements’, but you couldn’t transform elements into each other and you couldn’t turn them into anything else without mixing in another element. It was an examination of chemistry and chemical reactions by John Dalton that really gave convincing scientific evidence for atom theory. He noticed that when combining the elements that were known about, there was a pattern in the way they combined. When mixing nitrogen and oxygen, for example, the nitrogen could “absorb” a certain amount of oxygen — or twice that amount — but never anything in between. This makes perfect sense when you realize that you’re either seeing a reaction into Nitrous Oxide, NO, or Nitrogen Dioxide, NO2 — there must be fundamental units of each gas that can only combine with each other in whole numbers. Mathematically, you’d call that discrete, rather than continuous.
Dalton himself came up with atomic weights, and it was noticed that they also had a great ratio relationship going on; everything was roughly multiples of the lightest element, hydrogen. So physicists began to propose the idea that the atoms of the heavy elements were made up of multiple hydrogen atoms. This sounds reasonable, but, of course, it’s not quite right.
Physics is a dank meme. Specifically, it’s that one ‘expanding brain meme’. Either you know exactly what I’m talking about or you haven’t a clue, so I’ll explain for the benefit of people who haven’t wasted much of their lives. In this meme, you have a series of artistic images of a human with a brain. Alongside them are captions that relate to some topic. The first image is a small brain inside the skull, and the caption is some (simple) observation. Then, as you progress deeper into the meme, the observations get more complex and the picture gets more elaborate, first with the brain lighting up, then with rays of light shooting out of the brain, and eventually with some kind of god-like figure having attained some incredibly high level of understanding. Here’s an example: physicists who use numbers, physicists who use letters, physicists who use greek letters, physicists who use tensor notation.
Yet this meme is all of physics. Physics is this meme. It is a series of explanations for reality that get gradually more advanced and detailed as you go along. In some ways, talking about whether it’s “wrong” or “right” misses the point: all models are wrong, but some models are useful. So in this example, maybe we’d have the first caption as ‘Everything is made up of elements’ — then ‘Elements are made up of indivisible atoms’ — and soon, we’ll have the atom being made of electrons, neutrons and protons; and then the standard model that explains what these are made of: and, possible, after that, string theory or quantum field theory. Each layer allows you to understand more, but it also grows more complex.
Okay, enough meme tangent. Meanwhile, in 1897, the physicist with the coolest name of all time — JJ Thomson — was investigating cathode rays. So people had noticed as soon as they were able to produce good vacuums by pumping the air out of glass containers — something weird happened if you tried to pass an electrical current through them. This was done by having different electrical charges on different ends of the tube — two electrical conductors. One was positively charged, the anode, and the other was negatively charged, the cathode.
The behaviour depended on how well you evacuated the tube. If the tube was partially evacuated, you could see sparks, or a glowing beam between the anode and the cathode. But as vacuum pumps got better, they were able to pump more and more air out of the tube. The scientists noticed a ‘dark spot’ appearing in front of the cathode, with no glow. As you pumped more and more air out of the tube, that dark spot grew until it filled the entire tube — but at the anode end of the tube, the glass itself would glow. Something invisible was travelling along the tube, carrying charge, and interacting with the anode end. These were called ‘cathode rays’, and had been studied for decades: but JJ was able to measure the mass of the cathode rays. He found that they were over a thousand times lighter than atoms, and negatively charged. What’s more, regardless of which material you used as the cathode or anode, the corpuscles were exactly the same in mass and charge. Cathode rays could be made to emit from all sorts of materials. So JJ Thomson proposed that these particles must also be a part of atoms. Thomson wanted to call them ‘corpuscles’, showing that despite having a cool name himself he had no idea about naming particles… but the name that stuck was electrons.
So we’re getting closer to the truth of what the atom is. Physicists by 1904 had figured out that it must contain some negatively charged electrons, and also some positive charge as well, because atoms were overall electrically neutral — they weren’t deflected by electric and magnetic fields like charged particles were. But physicists still hadn’t discovered the proton; instead, they thought that perhaps the atom was a positively charged lump of matter with some spread-out electrons embedded in it to keep the charge overall neutral. This is called the plum-pudding model — although in Thomson’s case he had correctly figured out that the electrons must be orbiting in some way.
The plum-pudding model had some obvious problems, and wasn’t universally accepted. Hantaro Nagaoka was a Japanese physicist who suggested an alternative model — where the electrons orbited around the heavy, central, positive charge like the rings of Saturn. This is closer to the truth, but the astonishing aspect of atomic physics hadn’t yet been realized.
The plum-pudding model was blown out of the water by the famous experiments conducted by Ernest Rutherford, Hans Geiger, and Ernest Marsden. They wanted to use radiation to probe the structure of matter. Listen back to ‘Unusually Hot’ where we discuss all the different types of radiation; the kind they used were alpha particles. As we discussed then, alpha particles are helium nuclei — they have 2 protons and 2 neutrons, and therefore they’re positively charged. Beta particles aren’t just alpha particles that don’t work in finance and own shabbier cars. They’re electrons, too. The confusing names in physics all tend to arise from misunderstandings like this.
So in Thomson’s model of the atom, the positive charge is spread out or diffused across the atom. Geiger and Marsden set up the experiment to bombard some gold foil with alpha particles. Now, in your high-school physics class and mine, what you often hear is “and then all of the alpha particles flew straight through the gold foil, confirming that the atom was mostly empty space!” But this isn’t what really happened. Because — Geiger and Marsden already knew that alpha particles could penetrate through thin layers of foil. That’s why they made the foil thin in the first place. The point was this idea that you could measure the charge distribution on the atom by seeing how much they were deflected. They’d done the calculations, and they were expecting to see tiny deflections for the alpha particles that passed close to atoms — the positive charge on the plum-pudding atom would repel the alpha particle, and deflect it by a small amount.
The really crucial thing they observed wasn’t that many of the alpha particles went straight through the foil. This was expected. Instead, what they saw was that some alpha particles were deflected by ridiculous degrees, and shot out at right angles — or even, sometimes, right back at the incredibly dangerous radium sample they used as an emitter. They had as a detector set up a ring of fluorescent paper — the only way you could see the alpha particles was from a tiny flash when they hit the detector paper. Rutherford was a wily old dog, and left the laborious job of counting these flashes — which took hours — to Geiger and Marsden. Perhaps this experience of manually counting particles motivated Geiger to develop his Geiger counter for automatically counting radiation. But they must have been motivated by what they saw on the near side of the ring: the occasional, impossible flash.
When Rutherford found out, he uttered one of those famous physicsy quotes:
“It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
What Rutherford realized is that there must have been some ‘head-on’ collisions, where the alpha particles were essentially directly striking something very small — hence the low probability of deflection — and very densely charged. It’s important to understand that the electric field at a surface depends on the density of the charge — its concentration — and not the total amount. So you can get these mad deflections of 90 degrees or more with a very powerful electrical field that’s concentrated in a small area — the spread-out, diffuse positive charge of the plum pudding model could never do that.
The experiment allowed Rutherford and his colleagues to estimate the size of the small, positively-charged nucleus at the heart of the atom. Rutherford realized that it was so small that you could effectively treat it as a point at the heart of the atom; and we now know that — depending on the atom — the nucleus is 20,000–145,000 times smaller than the atom overall in length. In terms of the volume it takes up, you have to cube that. This is what leads to all of those great analogies like, if the nucleus was a pea, the atom would be the Sistine Chapel, or whatever. Here’s one I worked out: if the nucleus is a golf ball, the hydrogen atom as a whole extends across more than five golf courses.
So in Rutherford’s model, the electrons orbit around the central, tiny, positively charged nucleus. They’re pulled in by the attractive electromagnetic force between the electrons and the nucleus, just like planets orbiting around the Sun; it provides that force towards the centre that allows them to accelerate. And later, physicists would discover that the nucleus was made up of the positively-charged protons, and the neutrally-charged neutrons, which in some ways acted like a glue sticking the whole thing together. Finally, we have Democritus’ atoms; the indivisible proton, neutron, and electron; and, in various combinations, these fellas can make up any element you like. This picture — of electrons whizzing around a nucleus (although it’s never drawn to scale, because then you’d never see the nucleus) is one of the most familiar images in all of physics. It’s also completely physically impossible.
Physicists already knew at that time that if you have an accelerating charge, it radiates energy. We discussed this in our episode on electromagnetic radiation — do you remember the wiggling electrons that produce the light that we see in the world around us? And, of course, this same phenomenon causes the Northern Lights — charged particles from outer space — to produce that wonderful glow when they’re accelerated in the Earth’s magnetic field. But that glow is energy. So there’s a very scary question. If these electrons are orbiting around the positively charged nucleus, they’re constantly being accelerated. They should be radiating, which means the electron should be emitting energy constantly, which means it should be losing energy, which means it should spiral into the positively charged nucleus and decay. Which means atoms aren’t stable. Which means they can’t exist. So what the hell is going on?
The answer to this question is: quantum mechanics. And yes, we will get there — soon. But I really want to lay down loads of classical physics first, so that I can refer back to it and explain how quantum messed everything up. But I hope you’re beginning to see why physics is an expanding brain meme. There are layers and layers, and we’re still not at the bottom.
Thanks for listening to this episode of physical attraction. Next episode we’ll get onto the full standard model of particle physics. You’re not going to want to miss it!
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How to conceal a Hadron: Particle Physics and the Standard Model
So last episode I made all kinds of wild promises about getting to the Standard Model — and then we detoured into atomic physics more generally because I wanted to make sure we were all on the same page. So this episode sort of follows on from that, but you can listen to it as a standalone show: I’ll start with the particles that make up the atom, protons, neutrons, and electrons.
But as we’ve discussed, in 1936, the muon was discovered — a sort of short-lived, heavy electron — in cosmic rays: prompting the famous response — who ordered that? It turns out there were lots of other particles that needed to be explained. In one area of physics, cosmic rays were being examined using cloud chambers. These are the subatomic particles that are constantly bombarding Earth from outer space. A cloud chamber contains supersaturated vapour; when a charged particle passes through, it knocks electrons off atoms and the resulting ions cause little droplets of vapour to condense around them — leaving a track of ‘clouds’ behind them. These little trails, visible to the naked eye but left by tiny subatomic particles, have characteristic shapes. The heavy, blundering alpha particle leaves a short, thick, straight track. Electrons are lighter and less ionizing; their trails are thinner, and they’re deflected more by collisions, electric and magnetic fields, as well as travelling further. These kind of experiments discovered all sorts of particles, including one with the same mass of the electron that carried the opposite charge; the muon — and in the 1940s, weird particles called “kaons”, and “pions”.
Physicists had managed to realize that “alpha” radiation was the same as a helium nucleus, and “beta” particles were electrons or positrons. But there were still some unsolved problems about the nature of beta decay. It seemed to the physicists that radioactive beta decay, which was observed in some unstable atoms, involved a change. A neutron emitted an electron, and became a proton. But this couldn’t be the whole picture, because neutrons — when isolated — decayed themselves.
We now know that neutrons are part of most nuclei, but when they were first discovered, it was as yet another form of particle radiation. This radiation was more penetrative than alpha particles, but didn’t bend in magnetic fields; physicists initially thought it might be gamma rays, but it was later proved to be a particle: the neutron.
If you have an isolated neutron that’s sitting more or less still, it decays with a half-life of 885 seconds. That means if you have a pile of neutrons, on average, half of them will have decayed after around 15 minutes. When they decay, we can see protons and electrons emerging. But there is an issue with this picture. You can’t have one particle splitting into two and always conserve both energy and momentum. (that momentum is kind of like a measure of how much stuff is moving in a given direction — it’s similar to the mass times the velocity.)
Realizing this isn’t so difficult. Let’s say we have a neutron sitting still and it splits into an electron and a proton. There’s no overall momentum before the decay, so there must be no overall momentum after the decay. This means we need the final momentum of the electron and the proton to be equal and opposite. The problem is, because the mass of the electron is so different to that of the proton, there’s no way to conserve energy and momentum with just two particles. The sums don’t work out. You can fix them if you have a third particle that’s created in the decay — one that can carry off the extra energy and momentum. Then you can get the range of different speeds, energies and so on that physicists observed when neutrons decayed.
Enter Wolfgang Pauli. One of the giants of quantum mechanics, he was also famous for his acerbic personality. His colleagues coined the term “The Pauli Effect” for his mysterious ability to break experimental equipment simply by being nearby; Pauli was a true theoretical physicist and loved this little coincidence. He was a perfectionist who had little time for anything he considered to be incorrect, which is the kind of attitude you can only get away with if you’re a genius. But worse than things that were incorrect were those things that were so unclear they offered no testable predictions. For a paper like this, he offered the pretty grim conclusion: “It’s not even wrong.” Ouch.
I didn’t know this until researching this episode, but Pauli actually introduced the idea of the neutrino in a letter that began: “Dear radioactive ladies and gentlemen…” In this letter, written in 1930, he expressed hope that the physicists he was writing to would be able to directly detect the neutrino and confirm this theory: which makes sense — if it couldn’t be tested, then it was ‘not even wrong.’ In fact, when fellow physicist Enrico Fermi submitted a neutrino paper to Nature, arguably the most famous journal out there, they rejected it, saying it was “too remote from reality”.
You can see why people might be sceptical about the neutrino. It seems very convenient that there’s another particle that just exists to carry away excess momentum and energy, that’s too small to be detected with current technology. But Pauli was vindicated when the neutrino was observed in 1956, twenty-six years after he’d first posited it as an idea. It was just a couple of years before Pauli died, and he reportedly said: “Everything comes to him who knows how to wait.” And then it took them another forty years to award the people who discovered the neutrino with the Nobel prize, which happened in 1995. Those who can wait, indeed.
Neutrinos are weird. They are ghostly particles, incredibly difficult to detect. If you don’t believe me, consider that — right now, as you listen to this — a hundred trillion neutrinos are streaming through your body. Most of them come from the sun, which rains down an astonishing 65 billion neutrinos on every square centimetre of the Earth every second. They’re so reluctant to interact with matter that almost all of them pass straight through the Earth and flow out through the other side. It used to be thought that they had no mass, because they were travelling at almost the speed of light — so close that it’s basically indistinguishable. We now know that they do have a mass, but it’s really, really tiny: so tiny that all of the neutrinos that will pass through your body across the course of your entire life wouldn’t weigh more than a billionth of a gram (and possibly much less than that.)
So how do you detect something that can happily pass through the entire Earth without ‘hitting’ anything? You get lucky. If you want to measure these neutrinos from the Sun, one of the methods is to use a big vat of water — a thousand tonnes of the stuff was used at the Sudbury Neutrino Observatory in Canada. They actually use ‘heavy’ water, which is slightly radioactive. Heavy water is like normal water, H20, but the hydrogen is a different isotope. Isotopes of an element are the same element, but with different numbers of neutrons in the nucleus. Normal hydrogen has just a proton in the nucleus, but in heavy water, the hydrogen has a proton and a neutron. This is good for neutrino detection.
See, what can happen — albeit with low probability — is kind of the opposite of a beta decay. I like to think of a neutrino as a bit like the ghost of an electron, or maybe a sort of electron shell. A neutrino can interact with a neutron and turn into an electron, leaving behind a proton. So it’s neutrino + neutron turns into proton + electron. This is the type of interaction that — rarely, but possible to detect — occurs with these huge vats of heavy water. It turns out that neutrinos can interact with electrons and nuclei as well via what’s called the “weak nuclear force”; they’re called weakly interacting for that reason. And, as the name suggests, these ‘weak’ interactions don’t happen all that often.
So you might be thinking: if muons are like heavy electrons, do they have similar interactions? Yes, it turns out, they do. Muons have their own “muon” neutrinos, which can be turned into muons through a weak interaction. And, we’re going to jump a bit in time here, but in the 1970s another particle was discovered — the Tau particle. This has the same charge as the electron, and the muon, but it’s way heavier than both of them and way more unstable. Electrons essentially live forever. Muons live for a couple millionths of a second. Tau particles live less than a trillionth of a second before they decay. And Tau particles have their own Tau neutrinos as well. All of these particles are called leptons, and we call them the three generations of matter — the electron generation, the muon generation, the tau generation.
At this point, you’re beginning to see why everyone is saying — oh, my God, who ordered that? And you might be thinking — how do we know that the electron, the muon, and the tau are really it? How do we know that there aren’t just heavier and heavier, and less and less stable particles — more generations of matter — forever?
It’s a good question. But we can be pretty sure that there are just three, because, presumably — if there was going to be a generation of matter even heavier than the tau, there would need to be a pretty hefty neutrino to go along with them — and we’ve looked at the decays of heavy particles and found no such neutrino. CERN have said that there’s a 99.99999% probability that these are the only leptons that exist, although we should know by now that physics kinda has a way of throwing up new and inconvenient particles.
So. Recap. Here we are. Three generations of leptons, electron, muon, tau, and their neutrinos. Oh, and I haven’t mentioned it so far, but you’ve remembered that every particle has its antiparticle, right? Same is true for electron, muon, tau, and all of the neutrinos. They all have antiparticles.
Alongside the proton and the neutron, you sort of have a model here. But there are all of these weird kaons and pions to explain from the cosmic rays and the particle accelerator experiments that were starting to happen more and more in the 20th Century. More and more particles were getting added to the particle zoo; the delta particles, the omega particles, the sigma particles… they were all incredibly unstable, they had different charges (although always multiples of the they could all be found in particle accelerator experiments or sometimes cosmic rays, and it seemed like there was no end to them. In the 1950s, a physicist Murray Gell-Mann organised them into groups — and later, he came up with a theory to explain these groups. Protons, neutrons, and all of these particles they were finding weren’t really fundamental at all. They were made up of something else — quarks.
So: pronunciation. I’m going to pronounce it kwaaaarks. And this is CORRECT, because he nicked the name from famous doorstop and impenetrable self-appointed NOVEL Finnegan’s Wake, which includes — alongside a whole bunch of other stuff — the phrase “Three quarks for Muster Mark.” And unless you pronounce “Mark” and “Mork”, you can’t pronounce “quark” as “quork”. There we go.
So the quark model — the idea that all of these particles that were being discovered were made up of something else — could explain a lot of the properties that were observed. Some of the particles they’d seen decayed only via the weak interaction, and had slightly longer lifetimes; and they were called strange particles. With the quark model, you could say, okay — all the strange particles have a strange quark.
The quarks also needed to explain the charges of the particles. Every particle discovered had some multiple of the electron charge, just like the proton — this unit of charge was thought to be fundamental. This was really more of a maths puzzle than a physical puzzle. This is because the quarks weren’t discovered in an experiment, like other subatomic particles. Instead, they were proposed as building blocks that could explain the zoo of particles that had been observed. So, to explain all the charges, they needed to have an up quark — that was positively charged, with a charge of (2/3) — and a down quark — negatively charged, with a charge of -1/3. The strange quark, that was found in the strange particles, needed to be negatively charged, with -1/3 as well. And all these quarks also had antiparticles, with their opposite charge.
It’s really very similar to how the periodic table of the elements was organized. They had a set of elements of various masses and charges that could be explained by considering a nucleus. Organizing the elements by their properties and weights allowed the early chemists to spot the patterns and understand the rules that the underlying structure would have to obey. And that’s exactly what happened with the hadrons — sorting them made it clear that there must be quarks, and the properties that the quarks needed to have.
This was great, of course. Now you could see that the proton was made of two up quarks and a down quark, which added up to 1. A neutron must be one up and two downs, adding up to zero. Physicists quickly realized that the particles they’d been seeing were of two types. There were some which had three quarks — and these got called baryons. I have a joke with my physics friends, because we have no lives, that everything in physics is named after a guy called Barry. So, you know, quarks were discovered by Barry Quark, electromagnetism was discovered by Barry Electromagnetism. It’s an inherently comical name. So I guess in this scheme, baryons were discovered by… Barry Baryon.
Some of the other particles, like the pions, could be explained if they were made up of a quark and an antiquark. These particles ended up being called mesons. And all of the particles made of quarks together are called hadrons, because, you know, particle physicists just love naming things. That’s what they love the most.
But… you’re not going to be surprised to hear me say this… these three quarks were not the end of the story, and it turned out there was another generation of unstable, heavy quarks! Just like the case with electrons and muons. But the top quark is ridiculously heavy — it has the mass of an entire atom of gold, which is made up of over 100 first-gen quarks. These three quarks… people weren’t sure what to call them at first. They briefly went with “truth, beauty, and charm” but only “charm” was charming enough to stick around. This charming quark. Truth and Beauty ended up with the less poetic names of top and bottom. But at least you can see this way that the top quark is like a heavier up quark; the bottom quark is like a heavier down quark… and, um, somehow if you take something strange and make it way heavier, it’s suddenly charming. Whatever. Six quarks. And we don’t think there are any more.
So — there are some rules for how you can combine quarks that I won’t bore you with. Basically, for some reason, Nature won’t let us have charges that aren’t multiples of one electron.
So now we have another part of the standard model pretty much all nicely set up. Before, we had our leptons; the electron, muon, tau, and their neutrinos. Now we see that proton, neutron, and all the weird unstable hadrons out there are made up of quarks: the up, down, strange, top, bottom, and charm quarks. These can combine in groups of three to give you baryons. Or you can have quark and antiquark to give you a meson.
By the way, I can’t resist mentioning this: lots of mesons are bound pairs of a quark and its anti-quark. They can be produced in particle accelerators like the Large Hadron Collider, and show up at a specific set of energies. These particles, which live for a short time, are called quarkonium — depending on the flavour of the quark. So while charm-anticharm pairs are called charmonium, which sounds wonderful, bottom-antibottom pairs are called bottomonium. Which does not sound so wonderful.
With the quarks, we’re nearly there, but there’s a whole additional branch that we need to add to the family to get the standard model probably nailed down. And then, my dear sweet children, after wading through all of this with me, we can get finally get down to our BDSM.
But first, a little more about quarks. Because quarks are pretty quirky. They do have masses, but their masses don’t add up to the things they make up. So the mass of a proton is not the mass of two up quarks plus the mass of a down quark. This is because mass is really energy — and the quarks have some energy associated with them because of the force that draws them together. This force is called the strong nuclear force.
And the strong nuclear force is really, really strong. It’s so strong, in fact, that it’s impossible to separate a quark from its fellow quarks. They love being together. They cling to each other. We think it’s physically impossible to see a quark on its own. If you try to separate them, by applying some kind of brute force, you find that the energy required to do so is a huge amount. And, in fact, that energy is enough to create another pair of quarks. As you pull the quarks further and further apart, rather than getting a free quark, the energy literally produces two more quarks that combine with your existing quarks. Rather than producing free quarks, you’ve just made more hadrons. This is why physicists can only infer what quarks are really like by bombarding hadrons — you can’t ever get one in isolation.
In the next episode, we’re going to talk about the final components of the Standard Model — the force carriers. We’ve already discussed each of the four forces in this episode: gravity, the weak and strong nuclear forces, and electromagnetism. It turns out that at least three of these have particles associated with them. We’re going to get deep into the Standard Model and hopefully tie up all the loose ends, and then — if there’s time, we’ll talk about BDSM.
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BDSM: I’m Sparticle!
Hello and welcome to this episode of Physical Attraction! We have been talking about the Standard Model of particle physics, and here’s we’ve got to so far.
Everything is made up of fundamental particles. You have the leptons: that’s the electron, muon, tau, and their ghostly neutrinos that help us to conserve momentum. You have the quarks, which make up all of the hadrons. The up, down, and strange quarks: and their heavier cousins, the top, bottom, and charm quarks. Mixing quarks can give you baryons, like the proton and neutron. It can give you mesons, like the pion particles.
But you also have four forces.
There’s gravity, which pulls on everything with mass. There’s electromagnetism, which pulls on everything with charge. There’s the weak nuclear force, which is involved in the decay of neutrons and other particles, and it’s also how the ghostly neutrinos interact. And, finally, there’s the strong nuclear force: which binds the protons and neutrons together in the nucleus, and binds the quarks within each proton and neutron.
It turns out that the final part of the Standard Model is associated with these forces. Because, although we can imagine force fields that extend throughout space like Maxwell did, it turns out that forces have ‘carriers’. In some sense, when one particle exerts a force on another, another particle jumps between them to spread that influence. These force carriers are bosons. (That’s actually a name that relates to their spin, but I’ve got away without mentioning spin so far so I’ll be damned if I’m going to mention it now.)
In the case of electromagnetism, we know that particle already. It’s the photon, the unit of electromagnetic radiation. This, at least, in the world of particle physics kinda makes sense. Electromagnetic particles for the electromagnetic god.
In the case of the strong force, it’s something called a gluon. In keeping with the big family of quark, there are also eight different types of gluon; and they obey their own rules. Essentially, quarks and gluons have their own kind of charge — a bit like the electromagnetic charge, except there are three versions. Physicists have ridiculously called this the “colour charge” and the theory that describes it is called quantum chromodynamics. So there are red, green, and blue charges — and each of these charges has an anti-form as well. Between them, the colour charges explain how you can get the different gluons, and they explain how you can get the different rules for combining quarks. All good there.
Like quarks, you can’t really get a gluon on its own. Although there are some exciting things that physicists are hoping to create in particle colliders that are theorized to exist, but have never been observed. So, notice that the gluons themselves — that carry the strong force — are also charged with the charge of the strong force! This is unlike electromagnetism. The photon, which carries electromagnetic forces, is not a charged particle. But since the gluons have this strong type of charge, they can interact with each other and form something called a glueball. Physicists have found some things that might be glueballs, but they aren’t sure yet.
So much for the strong force. In the case of the weak force, you get three force mediators for the price of one. There are the W bosons, which have positive and negative charges, and the Z boson, which has no charge.
W and Z bosons are massive beasties. They’re heavier than whole atoms of iron, which is why it took particle colliders running at huge energies to finally produce and observe them in the 1980s.
The W boson finally makes sense of that issue we discussed in the last episode. Neutron decay.
We talked about how a neutron, with charge zero, can decay into a proton, with charge one, an electron, and a neutrino. Now we see what actually happens. In the neutron, there’s two down quarks and an up quark. In the proton, two ups and a down. So what occurs is a down quark emits a W minus boson, and turns into an up quark. The neutron has therefore turned into a proton. The W boson travels a tiny distance, and then decays into an electron and electron neutrino, which is all we see. Now you can see how the weak interaction can change different kinds of quarks into each other, and this is how weakly interacting particles decay.
As well as being massive, the W and Z bosons also have tiny lifetimes — 10^-25 seconds. That’s 1 divided by 1 with 25 zeros after it. Really, staggeringly small. Before we move on, there’s an amazing fact about the lifetime of the W boson which I have to share.
Because, like so many other things in physics — if it were slightly different, there’s no way we could be here. If the W boson lived slightly longer, the weak nuclear force would be too strong, fusion in the Sun would occur too quickly, and the Sun would have burned out before life could evolve. If it lived for a slightly shorter amount of time, the weak force would be too weak, and you could never have stars at all. This is one of the many examples of a problem called Fine-Tuning. But that’s for another episode.
So there are just two loose ends to tie up on this description of the standard model. And then, finally, finally, we can get onto BDSM as I’ve promised you for so, so long.
We’ve dealt with three forces — but what about gravity? Is it also mediated by its own force particle?
Gravity is weird. And the failure to marry a working theory of gravity into our working theories for the other forces is a major weakness in current physics. Some theories pose that gravity should have its own particle, the graviton. But the graviton has never been observed. Some models predict that, to observe even one, you’d need a detector the size of Jupiter to run for ten years — so it’s not likely that we’ll find a graviton soon. Understanding how gravity works with the Standard Model, or with our ideas about quantum mechanics, is pretty much the unsolved physics problem. It’s been that way for decades. Answers on a postcard, guys.
So, leaving the most difficult problem in physics for another day, we’ve also got the last piece of the current Standard Model puzzle — the Higgs boson! Arguably one of the most famous celebrity particles in the world. See, the Standard Model is not just a list of particles as I’ve described — it’s a set of equations and symmetries as well. These symmetries, without the Higgs, predict that everything should be massless. We’ve talked about symmetry before, and in some ways, there’s nothing more symmetrical than zero. Nothing is nothing, everywhere you go. Which is a big problem, because photons are massless, but nothing else is. And the Standard Model without the Higgs can’t explain why all of these subatomic particles have the masses that they do. If you just inject the masses in as extra parameters for the model — the energies of the different particles — then you come into other problems, things the theory can’t explain. There needs to be something else — a Higgs field, which allows the particles to have mass. All of the different subatomic particles react with the Higgs field in different ways; the symmetry is broken, and they’re allowed to have different masses.
It’s a little strange to accept something like this. There’s another field — one that we barely interact with, but that’s nonzero everywhere, one that gives everything its mass, but isn’t gravity? The fact of the matter is: Higgs theory makes predictions that we’ve found to be correct. It explains things that other theories don’t explain. And when physicists found the Higgs boson in 2012, more than fifty years after it had theoretically been proposed, it confirmed that the Standard Model was correct.
So. We have our leptons: electron, muon, tau and their neutrinos. Six quarks that you can mix up in a bazillion different ways to get hadrons of all kinds. We’ve got four forces, three of which have nice particles explaining them: the gluons for the strong force, the Ws and Zs for the weak force, the photons for the electromagnetic force. The Higgs dots the eyes, crosses the ts, and gives the particles the mass-energies that they have. And we’ll just sweep gravity under the MASSIVE PROBLEM carpet. That’s the Standard Model. You’re a particle physicist now. We got there. And it’s right. Sort of.
It might be correct in the sense that all of these things — the gluons, the quarks, the Higgs, the leptons and the hadrons, the photons, all of it: we have seen all of them. We have mathematical models for all of them that make good predictions. We can tell you how they are going to interact, and then observe the interactions in nature. It’s really, really astonishing that we’ve been able to do this. And, if you’ve listened to the last three episodes, you’ll see that this was a journey that took thousands of years of human thought (admittedly accelerating pretty rapidly towards the end.)
It’s correct. But it’s incomplete. We know that it can’t explain gravity. And we also know that there are big ranges of energy that we haven’t probed yet — and there are probably all kinds of things that we haven’t yet discovered. They could be bizarre, exotic forms of matter that will need new theories to describe. Just recently, physicists announced tentative evidence of finding something called a “pentaquark” — that’s five quarks bound together in a way we weren’t sure was possible before.
And there’s another fact. If you’ve been paying careful attention you’ll notice there was a change in how we talked about the discoveries of these different particles as we moved through time. In the old days, with the cloud chambers and the bubble chambers, experimental physicists would find a new particle. The theorists would be all happy and smug, like, “yes we have explained everything now”, and then the experimentalists would say — oh, but the atom’s not like that, kinda looks like it’s mostly empty space now boss. Or: oh, but I found this, I’m calling it a muon, any ideas guys?
Theory and experiment, ideally, always have to go hand in hand in physics. The greatest examples of theories in physics are those which make accurate, testable predictions. When Einstein’s theory of general relativity was confirmed by experiment, it was a huge moment — even though it seemed likely that the theory was correct before any experimentation had been done. Quantum mechanics has some philosophical implications that disturb and upset some people: but its ability to predict the results of experiments is uncannily good, and that’s why it’s a well-respect theory.
But then at some point in the mid 20th century, things switched around. Pauli came up with the idea of the neutrino — and it took twenty odd years for the experimentalists to find one. Theorists came up with the W and Z bosons, and predicted the kind of energies they’d have: and then they sent experimentalists scrambling to find them. And theorists came up with the Higgs, and it took 50 years and one of the biggest experiments ever conducted for the experimentalists to catch up and finally detect the thing. So now, for the most part, theorists — motivated by the symmetry and the neatness of their theories — suggest new particles for the experimentalists to find. And this is where we get into physics beyond the standard model. BDSM, at long last.
One major mystery in cosmology and astrophysics is dark matter. We’ll get into it in another episode, but for various reasons we believe that up to 24% of the energy of the Universe could be concentrated in dark matter — a type of matter that doesn’t interact with electromagnetic radiation, and can’t be seen, but does interact with gravity. One of the ideas, then, is that dark matter is some new type of particle — perhaps a Weakly Interacting Massive Particle, or WIMP. WIMPs have been theorized for many decades now as part of the solution to this dark matter problem. It turns out that, if you model the early Universe, the number of WIMPs that would survive — due to the strength of the weak force — might *just* be the right amount to give us the dark matter we need; a coincidence (or piece of evidence, depending on how you feel about WIMPs) that is sometimes called the ‘WIMP miracle’.
The only problem is that we haven’t been able to observe WIMPs yet. Some theories predict that they should have masses of around 100GeV. I should explain at this point that particle physicists have a very unique way of expressing mass. As we say all the time, mass is really just a form of energy. And a voltage is a measurement of how much energy can be delivered to a charge. So, when one electron (with its electron charge) passes through a voltage of one volt, it gets one electron volt of energy. For a sense of scale, the energy of a photon of visible light is a couple of eV. The rest energy of an electron is around half a million eV, and a proton is about 940 million eV in mass. So 100GeV is 100 billion electron volts, or around 1/10th of the kinetic energy of a flying mosquito.
The only problem is that we found the Higgs boson at an energy of around 120GeV. The Higgs boson is not a good candidate for dark matter — it’s too unstable and couldn’t have the gravitational impact that dark matter has. If dark matter was a particle of around 100GeV, we’d expect to have produced it at the Large Hadron Collider, just like the Higgs. But we haven’t seen one yet. There’s also the question of whether we’d be able to observe WIMPs on Earth like we can see neutrinos. If WIMP theory is correct, there should be a background of WIMPs everywhere, flowing through the Earth and occasionally interacting — but no experiment has seen conclusive evidence of this. There are lots of experiments that are trying — some use incredibly cold crystals, kept at very low temperatures. The hope is that a WIMP will smash into the crystal and cause vibrations we can see — but no dice so far. As a result of 30+ years of searching turning out nothing, WIMPs are going out of fashion as dark matter candidates, although as they would be very difficult to detect it’s hard to say for sure.
One of the theories that particle physicists love the most is called Supersymmetry. And yeah, Arcade Fire did a catchy song about it before their latest album disappointed legions of die-hard fans. In that song, they sang “I know you’re living in my mind / It’s not the same as being alive”. If this was intended as a thinly-veiled criticism for the lack of experimental evidence of supersymmetry, then Arcade Fire are clearly geniuses, but I have a sneaking suspicion they just picked the word “supersymmetry” because it sounds cool.
But “because it sounds cool” is not a good enough reason in physics, otherwise we’d probably call them Death Rays instead of Gamma Rays. So what is supersymmetry and why do people think it might exist?
It’s unfair to say that the solution to every problem in physics according to particle physicists is just to add more particles. But supersymmetry suggests that — every particle we just spent the last three episodes learning about should have a partner superparticle, or sparticle.
That means electrons will have superelectrons, or selectrons. Superprotons would be sprotons. Meanwhile the bosons — remember, the force carriers and the higgs — have a different naming convention. Winos are the W boson superpartners; gluinos are the supersymmetric gluons, and Higgsinos are the supersymmetric Higgs partners. And some of these theories predict that there will be a fairly light supersymmetric particle that would interact weakly — just like a dark matter candidate would. So it’s *possible* that supersymmetry could explain dark matter.
You’re probably thinking: why have a partner for every particle when one particle would do? Well, it’s all motivated by a good deal of complicated mathematics that I won’t get into. In part because I don’t really understand it myself: this is the kind of thing you need to study particle physics to PhD level to really understand. But there are other physical, theoretical motivations for supersymmetry that we will go into.
For a start, we’ve talked about two broad classes of particles. You have your force-carrying bosons, like W Z photons and so on. And you have your fermions, which are neutrinos, electrons and also quarks etc. Quantum-mechanically, what makes them different is spin. Fermions have spin-1/2, 3/2, etc. and bosons have spin 0, 1, 2 etc. In supersymmetry, every boson has a partner that’s a fermion, and vice-versa. So the electron would have a boson partner called the super-electron. And the W boson would have a fermion partner in the Wino.
You can see that this removes the asymmetry in the sense that there’s no spin weirdness: there’s no set of particles that for some reason has ½ integer spin, and no other set that has integer spin. In the same way, the fact that every particle has an antiparticle kinda removes the asymmetry in terms of charges. It’s not that some particles are randomly positively charged and some are negative; it’s just that the half of particles that dominate in our Universe have these properties, if that makes sense.
Many grander theoretical theories require supersymmetry, mathematically, to work and to explain the Universe. And there’s also another major motivator for supersymmetry: something called unification.
It should be clear from the last few episodes if nothing else that we’re living in a very, very, weird universe. Why is there more matter than antimatter? Why are there all of these different forces and all of these different charges? Why are all of the forces different? Why are some of them stronger than others; why do some of them act over different distances than others? Why is there such an abundance of subatomic particles, and why are things like masses and lifetimes different? In other words, why aren’t things a hell of a lot simpler than they are?
There’s what is scientifically referred to as a ‘buttload’ of unanswerable why questions. But the main ones that frustrate physicists is: why aren’t things more symmetric? An idea is that, perhaps, at one point — at the very start of the Universe — they were. And there are reasons to believe this. It has been shown that, at hot enough temperatures — a thousand trillion kelvin, which is a basically a thousand trillion degrees Celsius — the forces start to unify. There is no distinction between the electromagnetic and the weak force. Instead, they become one force, one interaction — the electroweak force. This has been experimentally confirmed, and there are two Nobel prizes associated with it.
Physicists believe that at higher and higher energies, all of the interactions should unify. We live in a Universe where the symmetry is fundamentally broken — because of the low energy and temperature of the Universe, that mirror, that symmetry has shattered. Which leads us to see two forces where there’s only one, underlying force. You can see that when there’s more energy available, it’s possible to have lots of heavy W and Z bosons around as well as photons — having the extra energy to have a load of W and Z bosons is not a problem. But when the Universe cools down after the Big Bang — to below the typical energies of the W and Z boson — the symmetry is broken. Two forces that behave very differently — with different force-carriers and different ranges of action — when there should only be one.
At higher temperatures, the strong force also becomes unified with these three, and at even higher temperatures than that, gravity — that pesky gravity — should also become an aspect of the same, fundamental force. If things are hot enough, things can perhaps be simpler: all of the forces unify. The only issue is that this is all far beyond anything we can achieve in the lab. In fact, to get energies high enough for the gravitational force to come into the picture, we’d need experiments bigger than the entire planet Earth. I can’t see any hope of getting government funding for that any time soon.
But the point here is that we have, in electroweak theory, an example of symmetry breaking in the Universe. We know that at higher temperatures and energies, things are unified; and then, when you go below a certain threshold, the symmetry gets broken, things start having pesky masses, and so on. Most SUSY theories predict that a broken symmetry explains why we can’t see supersymmetric particles — they must have very high masses compared to their partners. At high enough energies, it’s obvious that everything is symmetric with its supersymmetry partner: in the same way as when you get high enough energies you can produce matter and antimatter particles equally. But in the low energies of the Universe we normally live in, the supersymmetric particles are frozen out of existence, somewhere in this unprobable higher energy regime.
Alongside this, it could explain aspects of the mass of the Higgs itself. I want to quote a brilliant article from Quanta Magazine, written by the brilliant Natalie Wolchover, edited slightly for clarity. The original article is called What No New Particles Means for Physics:
“The main reason physicists felt sure that the Standard Model could not be the whole story is that its linchpin, the Higgs boson, has a highly unnatural-seeming mass. In the equations of the Standard Model, the Higgs is coupled to many other particles. This coupling endows those particles with mass, allowing them in turn to drive the value of the Higgs mass to and fro, like competitors in a tug-of-war.
— — — — — — — — — — — — — -
Some of the competitors are extremely strong — hypothetical particles associated with gravity might contribute (or deduct) as much as 10 million billion TeV to the Higgs mass — yet somehow its mass ends up as 0.125 TeV, as if the competitors in the tug-of-war finish in a near-perfect tie. This seems absurd — unless there is some reasonable explanation for why the competing teams are so evenly matched.
[But with supersymmetry], every participant in the tug-of-war game has a rival of equal strength, and the Higgs is naturally stabilized. Combine this with the predictions about dark matter possibly being a superparticle, and the unification of the forces, and supersymmetry looks really attractive.
But these theories — where superparticles stabilize the mass of the Higgs — do make concrete predictions about the mass of the superparticles, and our experiments just don’t support them at the moment. Given that we haven’t found superparticles up to very high masses, the supersymmetry must be very broken. And the fear is that, ultimately, supersymmetry becomes so “broken” that the effects of the particles and their superpartners on the Higgs mass no longer cancel out, and supersymmetry fails as a solution to the naturalness problem. Some experts argue that we’ve passed that point already. Others, allowing for more freedom in how certain factors are arranged, say it is happening right now, with ATLAS and CMS excluding the stop quark — the hypothetical superpartner of the 0.173-TeV top quark — up to a mass of 1 TeV. That’s already a nearly sixfold imbalance between the top and the stop in the Higgs tug-of-war. Even if a stop heavier than 1 TeV exists, it would be pulling too hard on the Higgs to solve the problem it was invented to address.”
There are plenty of supersymmetric theories, but until we find evidence for one of them, it’s tricky to know for sure which one is correct — or even if the whole idea is correct. It could be that we’re barking up the wrong tree entirely.
Alongside the supersymmetric models, there are other things that the LHC is currently looking for. An example is — remember how atoms were fundamental, until they turned out to be made of protons, and protons were fundamental until they turned out to be made of quarks? Some physicists have proposed ‘preons’ that are the particles that make up quarks. It kinda reminds me of that old story about the rationalist who meets a believer in the theory that the Earth is a disc. Stephen Hawking quotes it in a Brief History of Time:
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on?” “You’re very clever, young man, very clever,” said the old lady. “But it’s turtles all the way down!”
In the case of particle physics, if we keep finding subunits, maybe it genuinely could be ‘turtles all the way down’ — or, at least, we haven’t yet got to the bottom of the finite turtle stack.
There are problems with preon theory, though. I guess the point is to simplify things beyond the Standard Model — to explain everything in terms of a new particle, new interactions. But you need more forces that govern preons, unlike anything we’ve ever seen. Plus, many preon models did not include a Higgs Boson — the discovery of the Higgs has discredited several of them. Perhaps the Large Hadron Collider could confirm that electrons or quarks have a finite size — which we haven’t been able to so far — which would indicate that preons may be real.
But this is really the silent tragedy of CERN and the Large Hadron Collider. They succeeded in their nominal mission — which was finding the Higgs Boson, and confirming what we know about the Standard Model. But what they really wanted to do was find something that deviated from the Standard Model — something that suggested that one of these supersymmetry theories, that could solve so many other unsolved problems in physics and are very mathematically elegant, might be true. And if supersymmetry is the explanation for dark matter, we probably would have seen those particles already.
The real fear is that, if we haven’t found any evidence for supersymmetry at CERN energies, then we won’t expect anything for quite some time. Of course, you see the problem for an experimentalist with a theory like supersymmetry: when does this symmetry breaking happen? If it happens at arbitrarily high energies, then we simply might never be able to reach them at all. The problem with particle physics is that — to find something new — you usually need to go up by a factor or 10, or 100, or even more. Creating a particle accelerator that’ll be hundreds of times more powerful than CERN — without the tantalising goal of the Higgs and the confirmation of the Standard Model to guide us — could be really, really difficult. Similarly, if CERN had found something — like the mysterious ‘diphoton bump’ that appeared in the results and then disappeared when they had more data — it would guide physicists as to which theories to pursue, and which experiments to design. It’s very difficult to know where to go when nature doesn’t give you any hints! So chances are most of the physicists working at CERN, while happy that they found the Higgs, will be concerned about the prospects for BDSM physics. As are we all. They still have a lot of data to go through, but it seems likely now that the announcements from the next few conferences at CERN will be: no news on supersymmetry. The theory may be beautiful; it may be wrong; either way, it may well be out of reach for us at the moment. But whatever other theory could arise to take its place, it will need to explain the problems with our current theories in the same way that supersymmetry does.
Okay. That’s probably enough BDSM for everybody.
Thanks for listening to this episode of Physical Attraction.
I hope you’ve enjoyed over the last few eps what has been an incredibly fast-paced, whistle-stop tour through atomic and particle physics. Next episode, we’re going to deal with something completely different: I don’t know what, yet, but I can assure you it’s going to be wild.
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